Solve Mixed Number Division: 9¼ ÷ 24/7 Step-by-Step

Q: Why do I need to convert the mixed number to an improper fraction?

Converting $ 9\frac{1}{4} $ to $ \frac{37}{4} $ makes division much easier! Mixed numbers have two parts (whole and fraction), but improper fractions let you work with just one fraction throughout.

Q: How do I remember to flip the second fraction?

Think "division becomes multiplication by the reciprocal". When you see ÷, change it to × and flip the second fraction. So $ \frac{37}{4} ÷ \frac{24}{7} $ becomes $ \frac{37}{4} \times \frac{7}{24} $.

Q: Can I simplify before multiplying?

Yes! Look for common factors to cancel. Here, you could cancel the 4 in the denominator with part of 24: $ \frac{37}{4} \times \frac{7}{24} = \frac{37 \times 7}{4 \times 24} $, but be careful with your arithmetic!

Q: How do I check if 259/96 is correct?

Multiply your answer by the original divisor: $ \frac{259}{96} \times \frac{24}{7} $. If you get $ \frac{37}{4} $ (which equals $ 9\frac{1}{4} $), your answer is right!

Q: Should I convert my final answer to a mixed number?

It depends on what the problem asks for! $ \frac{259}{96} $ is already in simplest form since 259 and 96 share no common factors. You could convert to a mixed number: $ 2\frac{67}{96} $.

Mixed Number Division with Fraction Multiplication

$+9\frac{1}{4}:+\frac{24}{7}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:05 Positive divided by positive is always positive

00:15 Convert mixed number to fraction

00:34 Substitute in our exercise

00:44 Division is also multiplication by the reciprocal

00:50 Switch between numerator and denominator

00:57 Make sure to multiply numerator by numerator and denominator by denominator

01:08 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$+9\frac{1}{4}:+\frac{24}{7}$

Step-by-step solution

Let's convert 9 and a quarter to a simple fraction:

$9\frac{1}{4}=9+\frac{1}{4}=\frac{9\times4}{4}+\frac{1}{4}=\frac{36}{4}+\frac{1}{4}=\frac{36+1}{4}=\frac{37}{4}$

Now the exercise we got is:

$\frac{37}{4}:\frac{24}{7}=$

Let's convert the division exercise to a multiplication exercise, and don't forget to switch the numerator and denominator in the second fraction:

$\frac{37}{4}\times\frac{7}{24}=$

Let's combine it into one multiplication exercise:

$\frac{37\times7}{24\times4}=\frac{259}{96}$

Final Answer

$\frac{259}{96}$

Key Points to Remember

Essential concepts to master this topic

Convert: Change mixed numbers to improper fractions first
Technique: Division becomes multiplication by reciprocal: $\frac{37}{4} \times \frac{7}{24}$
Check: Multiply final answer by divisor to get original dividend ✓

Common Mistakes

Avoid these frequent errors

Dividing without converting to improper fractions
Don't try to divide mixed numbers directly like 9¼ ÷ 24/7 = wrong answer! This creates confusion with whole and fractional parts. Always convert mixed numbers to improper fractions first: 9¼ = 37/4, then divide.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

Why do I need to convert the mixed number to an improper fraction?

Converting $9\frac{1}{4}$ to $\frac{37}{4}$ makes division much easier! Mixed numbers have two parts (whole and fraction), but improper fractions let you work with just one fraction throughout.

How do I remember to flip the second fraction?

Think "division becomes multiplication by the reciprocal". When you see ÷, change it to × and flip the second fraction. So $\frac{37}{4} ÷ \frac{24}{7}$ becomes $\frac{37}{4} \times \frac{7}{24}$ .

Can I simplify before multiplying?

Yes! Look for common factors to cancel. Here, you could cancel the 4 in the denominator with part of 24: $\frac{37}{4} \times \frac{7}{24} = \frac{37 \times 7}{4 \times 24}$ , but be careful with your arithmetic!

How do I check if 259/96 is correct?

Multiply your answer by the original divisor: $\frac{259}{96} \times \frac{24}{7}$ . If you get $\frac{37}{4}$ (which equals $9\frac{1}{4}$ ), your answer is right!

Should I convert my final answer to a mixed number?

It depends on what the problem asks for! $\frac{259}{96}$ is already in simplest form since 259 and 96 share no common factors. You could convert to a mixed number: $2\frac{67}{96}$ .

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